Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC approximation of the zero-norm including all standard sparse inducing penalty func...

Many tasks in imaging can be modeled via the minimization of a nonconvex composite function. A popular class of algorithms for solving such problems are majorizationminimization techniques which iteratively approximate the composite nonconvex function by a majorizing function that is easy to minimize. Most techniques, e.g. gradient descent, utilize convex majorizers in order guarantee that the ...

This paper concerns the problem of recovering an unknown but structured signal x ∈ Rn from m quadratic measurements of the form yr = ∣⟨ar,x⟩∣ for r = 1,2, . . . ,m. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal (m << n). We formulate the recovery problem as a nonconvex optimization problem where prior structur...

In this paper, we study a solution approach for set optimization problems with respect to the lower less relation. This can serve as base numerically solving by using established solvers from multiobjective optimization. Our strategy consists of deriving parametric family whose optimal sets approximate, in specific sense, that set-valued problem arbitrary accuracy. We also examine particular cl...

It is well known that the stochastic optimization problem can be regarded as one of most hard problems since, in cases, values f and its gradient are often not easily to solved, or F(∙, ξ) normally given clearly (or) distribution function P equivocal. Then an effective algorithm successfully designed used solve this interesting work. This paper designs bigger subspace algorithms for solving non...

Abstract We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce Frank–Wolfe (Fw) nonconvex and geodesically convex problems. present algorithms both purely finite-sum For latter, develop variance-reduced methods, including adap...

Quantum annealers aim at solving nonconvex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists of designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to i...

Sparse modeling has been highly successful in many realworld applications. While a lot of interests have been on convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are often challenging, especially for composite regularizers such as the nonconvex overlapping gr...

Nonconvex Stochastic Optimization stochastic optimization problems arise in many machine learning problems, including deep learning. The gradient Hamiltonian Monte Carlo (SGHMC) is a variant of gradients with momentum method which controlled and properly scaled Gaussian noise added to the steer iterates toward global minimum. SGHMC has shown empirical success practice for solving nonconvex prob...